A Linear-Time Algorithm for Finding Tree-Decompositions of Small Treewidth
SIAM Journal on Computing
SIAM Journal on Discrete Mathematics
Design networks with bounded pairwise distance
STOC '99 Proceedings of the thirty-first annual ACM symposium on Theory of computing
Small k-Dominating Sets in Planar Graphs with Applications
WG '01 Proceedings of the 27th International Workshop on Graph-Theoretic Concepts in Computer Science
Fixed-parameter algorithms for (k, r)-center in planar graphs and map graphs
ACM Transactions on Algorithms (TALG)
Decreasing the diameter of bounded degree graphs
Journal of Graph Theory
Improved approximability and non-approximability results for graph diameter decreasing problems
MFCS'10 Proceedings of the 35th international conference on Mathematical foundations of computer science
Augmenting forests to meet odd diameter requirements
Discrete Optimization
Operations Research Letters
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Given a graph G = (V, E) and an integer D ≥ 1, we consider the problem of augmenting G by a minimum set of new edges so that the diameter becomes at most D. It is known that no constant factor approximation algorithms to this problem with an arbitrary graph G can be obtained unless P = NP, while the problem with only a few graph classes such as forests is approximable within a constant factor. In this paper, we give the first constant factor approximation algorithm to the problem with an outerplanar graph G. We also show that if the target diameter D is even, then the case where G is a partial 2-tree is also approximable within a constant.